Fault Detection Filter Design Research Articles

Zonotopic fault detection for discrete-time systems with limited communication capability and sensor nonlinearity

In this paper, the fault detection filter (FDF) design problem based on a dynamic event-triggered mechanism (DETM) is investigated for discrete-time systems with signal quantization and sensor nonlinearity. In order to conserve the limited network resources, a newly event-triggered mechanism with dynamic threshold is adopted to reduce the number of transmitted data through network more effectively. With the consideration of DETM, signal quantization and sensor nonlinearity, a fault detection filter is constructed to achieve the robustly asymptotic stability of established model with expected fault detection objective. In addition, by influence of DETM, external interference and quantization errors, a zonotopic residual evaluation mechanism is constructed to detect the occurring fault of plant. Finally, a practical example is provided to illustrate the effectiveness of proposed design approach.

Hybrid-triggered H∞ Fault Detection for Distributed Time-delay Systems with Communication Quantization Based on T-S Fuzzy Model

In the network environment, the time-triggered mechanism wastes limited bandwidth resources due to the transmission of all sampled data to the network. The event-triggered mechanism may increase system errors due to ignoring factors such as changes in network utilization. In order to reduce the design conservatism, this paper studies the design of a hybrid-triggered H∞ fault detection filter for a class of nonlinear networked control systems described by Takagi-Sugeno (T-S) fuzzy model, and applies quantization techniques in the communication channel. Using the Lyapunov-Krasovskii functional and integral inequality methods, new results on the stability and H∞ performance of fuzzy fault detection systems are presented. In particular, the designed fault detection filter has a specific H∞ noise attenuation level γ. The final simulation results verify the effectiveness of the design.

Fault Detection Filter Design and Optimization for Switched Systems with All Modes Unstable.

This problem of intelligent switched fault detection filter design is investigated in this article. Firstly, the mode-dependent average dwell time (MDADT) method is applied to generate the time-dependent switching signal for switched systems with all subsystems unstable. Afterwards, the switched fault detection filter is proposed for the generation of residual signal, which consists of dynamics-based filter and learning-based filter. The MDADT method and multiple Lyapunov function (MLF) method are employed to guarantee the stability and prescribed attenuation performance. The parameters of dynamics-based filter are given by solving a series of linear matrix inequalities. To improve the transient performance, the deep reinforcement learning is introduced to design learning-based filter in the framework of actor-critic. The output of learning-based filter can be viewed as uncertainties of dynamics-based filter. The deep deterministic policy gradient algorithm and nonfragile control are adopted to guarantee the stability of algorithm and compensate the external disturbance. Finally, simulation results are given to illustrate the effectiveness of the method in the paper.

Event-triggered fault detection for T-S fuzzy systems with local nonlinear models in finite-frequency domain

This article investigates the issue of event-triggered fault detection (FD) filter design for T-S fuzzy systems with local nonlinear models. A novel FD filter subject to the event triggering transmission mechanism is designed in finite-frequency domain. Then, a novel lemma, in which the nonlinear part and the event triggering mechanism are dealt appropriately, is presented to capture the sensitivity and robustness performances. In addition, the slack matrices are utilised to derive optimal filter parameters by solving a convex optimisation problem. The less conservative FD method can get better detection performances than those entire-frequency methods. Finally, an example is introduced to verify the new results.

Dynamic event-triggered fault detection filter design for dynamical systems under fading channels

This article investigates the dynamic event-triggered fault detection filter (FDF) design problem for linear continuous-time networked systems, considering the fading channels phenomenon and randomly occurring faults. A dynamic event-triggered mechanism (ETM) is introduced to reduce the network bandwidth occupation more efficiently by utilizing an internal variable which can enlarge the event-triggered intervals. Besides, the Zeno phenomenon is eliminated fundamentally by ensuring that the event-triggered intervals are positive lower bounded. After that, sufficient conditions are derived to guarantee the stochastic stability of the residual system with a desired [Formula: see text] performance and the co-design criterion of the FDF and the dynamic ETM is developed. Finally, an unmanned surface vehicle (USV) system is used to illustrate the applicability of the presented approach.

Polynomial fault detection filter design under adaptive event-triggered scheme via line-integral Lyapunov functions

This paper investigates the problem of polynomial fault detection filter design under an adaptive event-triggered scheme for continuous-time networked polynomial fuzzy model–based (PFMB) systems considering network transmission delays. The proposed adaptive polynomial event-triggered scheme is checked only at the sampling instant to eliminate the Zeno behavior as well as save the network bandwidth. With the consideration of the mismatched membership functions (MFs), the asynchronous problem between the physical plant and the polynomial fault detection filter (PFDF) is examined. A Lyapunov–Krasovskii (L-K) function is introduced to deal with the time delays caused by the network transmission and the zero-order holder (ZOH), and a proper line-integral Lyapunov function is also introduced to reduce the conservation of the design constraints, whose analytical procedure is rule-dependent. The design constraints are given in the form of sum of squares (SOS) to keep the PFMB fault detection system asymptotically stable with [Formula: see text] performance [Formula: see text]. Finally, an inverted pendulum example together with a numerical example is given to verify the effectiveness and superiority of the proposed scheme in terms of transfer rate and conservatism.

Model matching fault detection filter design for a linear discrete-time system with mixed uncertainties

The paper discusses the design of a robust fault detection system for linear discrete-time invariant uncertain systems. The intended system consists of norm-bounded uncertainty, stochastic uncertainty, and external unknown input. Due to the mixed uncertainties, H ∞ based model matching technique is used to develop a robust system that offers maximum sensitivity to faults and minimum sensitivity to all other unknown inputs. Reference residual model is designed using co-inner-outer factorization and the fault detection system is designed so that the error between reference residual and robust residual generated by fault detection filter (FDF) is minimized in H ∞ sense. The existing condition of FDF is exploited in terms of linear matrix inequalities. A numerical example and a benchmark three-tank system are simulated to illustrate the performance of the proposed fault detection system. Results confirm the effectiveness of the proposed approach by timely detecting the occurrence of the fault.

Formula omitted] index for Itô stochastic systems with Possion jump

This paper studies the H− index problem for stochastic systems with Wiener processes and Poisson jumps. A necessary and sufficient condition is established for finite horizon Poisson jump stochastic systems to show that H− index lager than a given prescribed level γ>0 implies the existence of the solution of the corresponding generalized differential Riccati equation (GDRE). Accordingly, the corresponding results are extended to infinite horizon H− index problems for time-invariant square systems. As the direct application of our results, the fault detection filter design is realized in evaluating the fault detection performance.

Event‐triggered fault detection for discrete‐time Markovian jump systems in finite frequency domain

AbstractThis paper is concerned with the design of the finite frequency fault detection (FD) filter based on the event‐triggered scheme (ETS) for discrete‐time Markovian jump (DMJ) systems with Lipschitz functions, time‐varying delays, and packet dropouts. A novel FD filter subject to ETS and data missing is developed, and the augmented filter system is rewritten as a DMJ‐linear parameter varying (DMJ‐LPV) system through a reformulated Lipschitz property. Then, two novel lemmas are proposed to guarantee the DMJ‐LPV system robust to unknown disturbances and sensitive to finite frequency faults. Next, the proposed lemmas are deduced into linear matrix inequalities by using Finsler's lemma and S‐procedure. Finally, the application of Chua's circuit system is employed to illustrate the validity and superiority of the proposed theory.

Fault detection filter design for networked systems with cyber attacks

This paper focuses on the fault detection for networked systems with deception attacks. Firstly, a fault detection filter (FDF) is presented as a residual generator to detect the random occurring fault signal timely in networked systems with the consideration of network delay and deception attacks. Then, by using the Lyapunov stability theory and linear matrix inequality (LMI) techniques, sufficient conditions are presented to guarantee the stability with an H∞ performance index γ of our proposed fault detection system. Furthermore, the corresponding coefficient matrices of the FDF are also presented with the explicit expressions. Finally, two simulation examples demonstrate the effectiveness and practicability of the designed FDF.

Finite-Time Fault Detection Filter Design for T–S Fuzzy Markovian Jump Systems with Distributed Delays and Incomplete Measurements

Finite-Time Fault Detection Filter Design for T–S Fuzzy Markovian Jump Systems with Distributed Delays and Incomplete Measurements

Dissipativity-based asynchronous fault detection for T-S fuzzy nonlinear Markov jump systems subject to uncertain probabilities

In this paper, the dissipativity-based asynchronous fault detection problem over unreliable communication is investigated for a class of Takagi-Sugeno fuzzy nonlinear Markov jump systems with time-varying delays and subject to uncertain probabilities. The communication links between the plant and filter are considered to be unreliable, where the stochastic quantization and measurement missing phenomenon are taken into account simultaneously. The asynchronization between the plant and the designed fault detection filter (the random quantizer), is modeled by independent hidden Markov models with a conditional probability matrix, where both the transition probabilities of the plant and the conditional probabilities of the filter are considered to be only partially accessible. By virtue of the Lyapunov stability theory and the slack matrix technique, sufficient conditions guaranteeing the resulting residual system being asymptotically mean square stable and strictly (Q, S, R)-α-dissipative are deduced. And then, the parameters of the desired fault detection filter are explicitly expressed by solving a set of strict linear matrix inequalities. Finally, two examples are utilized to demonstrate the effectiveness and practicability of the proposed design technique.

Hybrid‐triggered fault detection filter design for networked Takagi–Sugeno fuzzy systems subject to persistent heavy noise disturbance

SummaryIn the network environment, the single time‐triggered scheme wastes limited bandwidth resources due to all the sampled data are transmitted to the networks, and the single event‐triggered scheme may increase system error because of ignoring factors such as changes in network utilization. To reduce the design conservatism, this paper is concerned with the hybrid‐triggered L1 fault detection filter design for a class of nonlinear networked control systems (NCSs) described by Takagi–Sugeno (T‐S) fuzzy model. Taking the effects of time‐triggered scheme and event‐triggered scheme into consideration simultaneously, we construct a fuzzy fault detection system. New results on stability and L1 performance are proposed for fuzzy fault detection system by exploiting the Lyapunov–Krasovskii functional and by means of the integral inequality method. Specially, attention is focused on the design of fault detection filter that guarantees a prescribed L1 noise attenuation level . Finally, two examples are presented to demonstrate the effectiveness of the proposed method.

Quantized Fault Detection Filter Design for Networked Control System with Markov Jump Parameters

In this paper, the design problem of fault detection filter for a class of networked control system subject to Markov jump parameters, randomly occurring uncertainties, sensor faults and packet dropouts by using state feedback control is investigated. The fault detection filter is used as an optimal residual generator that generates the residual signal and also guarantees the sensitivity of residual signal to the faults. To be more specific, a suitable threshold is selected for the residual evaluation function to reduce the error between the sensor faults and the residual signal. Further, by employing a fault detection technique along with output quantization approach, a new set of sufficient conditions is derived to ensure the stochastic stabilization of the addressed system with sensor faults under a predefined $$H_{\infty }$$ performance level. Particularly, by constructing Lyapunov–Krasovskii functional and utilizing extended Wirtinger-based single integral inequality, the required sufficient conditions are derived in terms of linear matrix inequalities for getting the required result. At last, two numerical examples including high alpha research vehicle model are presented to demonstrate the usefulness of our developed results.

Fuzzy filtering‐based fault detection for a class of discrete‐time conic‐type nonlinear systems

The authors investigates the problem of fuzzy fault detection filter (FFDF) design for a class of discrete-time conic-type nonlinear systems. By applying Takagi–Sugeno fuzzy models, the conic-type dynamic FFDF system is established. Then, utilizing the Lyapunov function method to find a sufficient condition which ensures that the conic-type dynamic FFDF system is asymptotically stable. After that, using linear matrix inequalities techniques, the FFDF design problem is transformed into an optimization algorithm. Finally, the simulation results demonstrate that the designed FFDF is effective for detecting the faults.

A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates

This work is concerned with the problem of full-order and reduced-order fault detection filters (FDFs) design in a convex optimization frame for continuous-time singular Markov jump systems (CTSMJSs) with complexity transition rates (TRs). A novel Lyapunov function construct approach is utilized to cope with the stochastic admissibility problem for CTSMJSs with complexity TRs. In order to obtain effective full-order and reduced-order FDFs, we decoupled the inequality using the presupposed Lyapunov matrix. Owing to the use of Lyapunov stochastic admissibility theory and a novel decoupling method based on convex polyhedron technique, some sufficient conditions are obtained to guarantee that the resulting full-order and reduced-order FDFs are suitable for CTSMJSs with complexity TRs. In particular, the reduced-order FDF has the advantages of small storage space and fast detection speed compared with the full order FDF. Four illustrative examples are given to explain the effectiveness of the proposed full-order and reduced-order FDFs design method.

Finite-Time Asynchronous Fault Detection Filter Design for Conic-Type Nonlinear Semi-Markovian Jump Systems

In this work, the problem of finite-time asynchronous fault detection filter design is investigated for conic-type nonlinear semi-Markovian jump systems with time delay, missing measurements and randomly jumping fault signal. In particular, the transition probability of the semi-Markov process is considered as time-varying along with lower and upper bounds of the transition rate. Besides, the asynchronous fault detection filter is developed for semi-Markovian jump systems with specific time-varying transition probability satisfying semi-Markov process. To quantify the effects of missing measurements a stochastic variable that satisfies Bernoulli’s distribution is adopted. Furthermore, a set of sufficient conditions is derived in terms of linear matrix inequalities (LMIs) by constructing proper mode-dependent Lyapunov-Krasovskii functional such that the augmented asynchronous fault detection filtering error system is stochastically finite-time bounded with prescribed strictly (Q,S,R)-γ dissipative performance. Finally, the provided filter designs applicability and usefulness has been verified with two numerical examples.

Spatial basis functions based fault localisation for linear parabolic distributed parameter systems

Fault localisation for distributed parameter systems is as important as fault detection but is seldom discussed in the literature. The main reason is that an infinite number of sensors in the space are needed to construct a distributed residual signal, which is nearly impossible in practice. In this study, a fault detection and localisation filter which only uses a finite number of sensors is initiated based on an approximated ordinary differential equation model. Considering the limitations on computation resources for higher-order models in practice, a novel set of spatial basis functions is applied to the reduced-order fault detection and localisation filter design. Under certain conditions, the novel spatial basis functions obtain smaller state truncation error while the order is lower compared to the mostly used eigenfunctions of the spatial operator.

Fault detection for a class of uncertain Lipschitz systems with time delays in finite‐frequency domain

This study investigates the problem of fault detection (FD) filter design for a class of uncertain Lipschitz systems with time delays, unknown faults, parameter uncertainties and bounded disturbances. A novel FD filter is proposed and the augmented filter system is converted to a linear parameter varying (LPV) system by the reformulated Lipschitz property. Then, two bounded real lemmas (BRLs) are given for the generated residual signal to achieve the fault sensitivity performance in low-/middle-/high-frequency domains and disturbance attenuation performance in the full-frequency domain. Next, the obtained BRLs are further converted into a set of linear matrix inequalities (LMIs) to implement the filter design. Finally, two illustrative simulations including a numerical example and Chua's circuit system clearly demonstrate the advantages of the developed FD scheme.

Robust fault detection filter design for a class of discrete‐time conic‐type non‐linear Markov jump systems with jump fault signals

This study investigates the robust fault detection filter design problem for a class of discrete-time conic-type non-linear Markov jump systems with jump fault signals. The conic-type non-linearities satisfy a restrictive condition that lies in an n -dimensional hyper-sphere with an uncertain centre. A crucial idea is to formulate the robust fault detection filter design problem of non-linear Markov jump systems as filtering problem. The authors aim to design a fault detection filter such that the augmented Markov jump systems with conic-type non-linearities are stochastically stable and satisfy the given performance against the external disturbances. By means of the appropriate mode-dependent Lyapunov functional method, sufficient conditions for the existence of the designed fault detection filter are presented in terms of linear matrix inequalities. Finally, a practical circuit model example is employed to demonstrate the availability of the main results.